chapter 17: stacks and queues

Chapter 17:Stacks and Queues

Objectives

• In this chapter, you will:– Learn about stacks– Examine various stack operations– Implement a stack as an array– Implement a stack as a linked list– Discover stack applications– Use a stack to remove recursion– Learn about queues– Examine various queue operations– Implement a queue as an array– Implement a queue as a linked list– Discover queue applications

2C++ Programming: Program Design Including Data Structures, Sixth Edition

Stacks

• Stack: a data structure in which elements are added and removed from one end only– Addition/deletion occur only at the top of the stack– Last in first out (LIFO) data structure

• Operations:– Push: to add an element onto the stack– Pop: to remove an element from the stack


Stacks (cont’d.)


Stack Operations

• In the abstract class stackADT:– initializeStack– isEmptyStack– isFullStack– push– top– pop


Implementation of Stacks as Arrays

• First element goes in first array position, second in the second position, etc.

• Top of the stack is index of the last element added to the stack

• Stack elements are stored in an array, which is a random access data structure– Stack element is accessed only through top

• To track the top position, use a variable called stackTop


Implementation of Stacks as Arrays (cont’d.)

• Can dynamically allocate array– Enables user to specify size of the array

• class stackType implements the functions of the abstract class stackADT



• C++ arrays begin with the index 0– Must distinguish between:

• Value of stackTop• Array position indicated by stackTop

• If stackTop is 0, stack is empty• If stackTop is nonzero, stack is not empty

– Top element is given by stackTop - 1


Initialize Stack


Empty Stack/Full Stack

• Stack is empty if stackTop = 0

• Stack is full if stackTop = maxStackSize


Push

• Store the newItem in the array component indicated by stackTop

• Increment stackTop• Overflow occurs if we try to add a new item to a full

stack


Push (cont’d.)


Return the Top Element

• top operation:– Returns the top element of the stack


Pop

• To remove an element from the stack, decrement stackTop by 1

• Underflow condition: trying to remove an item from an empty stack


Pop (cont’d.)


Copy Stack

• copyStack function: copies a stack


Constructor and Destructor

• Constructor:– Sets stack size to parameter value (or default value if not

specified)– Sets stackTop to 0– Creates array to store stack elements

• Destructor:– Deallocates memory occupied by the array– Sets stackTop to 0


Copy Constructor

• Copy constructor:– Called when a stack object is passed as a (value) parameter

to a function– Copies values of member variables from actual parameter

to formal parameter


Overloading the Assignment Operator (=)

• Assignment operator must be explicitly overloaded because of pointer member variables


Stack Header File

• Place definitions of class and functions (stack operations) together in a file– Called myStack.h


Linked Implementation of Stacks

• Array only allows fixed number of elements• If number of elements to be pushed exceeds array

size, the program may terminate• Linked lists can dynamically organize data• In a linked representation, stackTop is pointer to

memory address of top element in stack


Linked Implementation of Stacks (cont’d.)


Default Constructor

• Initializes the stack to an empty state when a stack object is declared– Sets stackTop to NULL


Empty Stack and Full Stack

• In a linked implementation of stacks, function isFullStack does not apply– Logically, the stack is never full

• Stack is empty if stackTop is NULL


Initialize Stack

• initializeStack: reinitializes stack to an empty state– Must deallocate memory occupied by current element– Sets stackTop to NULL


Push

• newNode is added at the beginning of the linked list pointed to by stackTop


Push (cont’d.)


Return the Top Element

• top operation: returns top element of stack


Pop

• Node pointed to by stackTop is removed– Second element becomes top element


Pop (cont’d.)


Copy Stack

• copyStack function: makes an identical copy of a stack– Similar definition to copyList for linked lists


Constructors and Destructors

• Copy constructor and destructor:– Similar to those for linked lists


Overloading the Assignment Operator (=)

• Overloading the assignment operator:


Stack as Derived from the class unorderedLinkedList

• Implementation of push is similar to insertFirst for general lists

• Other similar functions: – initializeStack and initializeList– isEmptyList and isEmptyStack

• linkedStackType can be derived from linkedListType– class linkedListType is abstract


Derived Stack (cont’d.)

• unorderedLinkedListType is derived from linkedListType– Provides the definitions of the abstract functions of the class linkedListType

• and derive linkedStackType from unorderedLinkedListType


Application of Stacks: Postfix Expressions Calculator

• Infix notation: usual notation for writing arithmetic expressions– Operator is written between the operands– Example: a + b– Evaluates from left to right– Operators have precedence

• Parentheses can be used to override precedence


Application of Stacks: Postfix Expressions Calculator (cont’d.)

• Prefix (Polish) notation: operators are written before the operands– Introduced by the Polish mathematician Jan Lukasiewicz in

early 1920s– Parentheses can be omitted– Example: + a b



• Reverse Polish notation: operators follow the operands (postfix operators)– Proposed by Australian philosopher and early computer

scientist Charles L. Hamblin in the late 1950s– Advantage: operators appear in the order required for

computation– Example: a + b * c becomes a b c * +



• Postfix notation has important applications in computer science– Many compilers first translate arithmetic expressions into

postfix notation and then translate this expression into machine code

• Evaluation algorithm:– Scan expression from left to right– When an operator is found, back up to get operands,

perform the operation, and continue



• Symbols can be numbers or anything else:– +, -, *, and / are operators, require two operands

• Pop stack twice and evaluate expression• If stack has less than two elements error

– If symbol is =, expression ends• Pop and print answer from stack• If stack has more than one element error

– If symbol is anything else• Expression contains an illegal operator



• Assume postfix expressions are in this form:#6 #3 + #2 * =

– If symbol scanned is #, next input is a number– If the symbol scanned is not #, then it is:

• An operator (may be illegal) or• An equal sign (end of expression)

• Assume expressions contain only +, -, *, and / operators


Main Algorithm

• Pseudocode:

• Four functions are needed:– evaluateExpression, evaluateOpr, discardExp, and printResult


Function evaluateExpression

• Function evaluateExpression:– Evaluates each postfix expression– Each expression ends with = symbol


Function evaluateOpr

• Function evaluateOpr:– Evaluates an expression– Needs two operands saved in the stack

• If less than two error– Also checks for illegal operations


Function discardExp

• Function discardExp:– Called when an error is discovered in expression– Reads and writes input data until the ‘=’


Function printResult

• The function printResult: If the postfix expression contains no errors, it prints the result– Otherwise, it outputs an appropriate message

• Result of the expression is in the stack, and output is sent to a file


• To print a list backward nonrecursively, first get to the last node of the list– Problem: Links go in only one direction– Solution: Save a pointer to each of node in a stack

• Uses the LIFO principle

• Since number of nodes is usually not known, use the linked implementation of a stack


Nonrecursive Algorithm to Print a Linked List Backward

Nonrecursive Algorithm to Print a Linked List Backward (cont’d.)


Queues

• Queue: set of elements of the same type• Elements are:

– Added at one end (the back or rear)– Deleted from the other end (the front)

• First In First Out (FIFO) data structure– Middle elements are inaccessible

• Example:– Waiting line in a bank


Queue Operations

• Queue operations include:– initializeQueue– isEmptyQueue– isFullQueue– front– back– addQueue– deleteQueue

• Abstract class queueADT defines these operations


Implementation of Queues as Arrays

• Need at least four (member) variables:– Array to store queue elements– queueFront and queueRear

• To track first and last elements– maxQueueSize

• To specify maximum size of the queue


Implementation of Queues as Arrays (cont’d.)

• To add an element to the queue:– Advance queueRear to next array position – Add element to position pointed by queueRear



• To delete an element from the queue:– Retrieve element pointed to by queueFront– Advance queueFront to next queue element



• Will this queue design work?– Let A represent adding an element to the queue– Let D represent deleting an element from the queue– Consider the following sequence of operations:

• AAADADADADADADADA...



• This would eventually set queueRear to point to the last array position– Giving the impression that the queue is full



• Solution 1: When queue overflows at rear (queueRear points to the last array position):– Check value of queueFront– If queueFront indicates there is room at front of array,

slide all queue elements toward the first array position

• Problem: too slow for large queues• Solution 2: Assume that the array is circular



• Deletion Case 1:



• Deletion Case 2:



• Problem:– Figures 18-32b and 18-33b have identical values for queueFront and queueRear

– However, Figure 18-32b represents an empty queue, whereas Figures 18-33b shows a full queue

• Solution?



• Solution 1: keep a count– Incremented when a new element is added to the queue– Decremented when an element is removed– Initially set to 0– Very useful if user (of queue) frequently needs to know the

number of elements in the queue



• Solution 2: Let queueFront indicate index of array position preceding the first element– queueRear still indicates index of last one– Queue empty if:

• queueFront == queueRear– Slot indicated by queueFront is reserved– Queue is full if next available space is the reserved slot

indicated by queueFront


Empty Queue and Full Queue

• Queue is empty if count ==0• Queue is full if count == maxQueueSize


Initialize Queue

• Initializes queue to empty state– First element is added at first array position– queueFront set to 0– queueRear set to maxQueueSize -1– count set to 0


Front and Back

• front operation: returns the first element of the queue– If queue is empty, program terminates

• back operation: returns the last element of the queue– If queue is empty, program terminates


addQueue

• addQueue operation:– Advance queueRear to next array position– Add new element to array position indicated by queueRear

– Increment count by 1


deleteQueue

• deleteQueue operation:– Decrement count by 1– Advance queueFront to next queue element



• Constructor:– Sets maxQueueSize to user specification– Creates array of size maxQueueSize (or default size)– Initializes queueFront and queueRear to indicate

empty queue

• Destructor:– Deallocates memory occupied by array


Linked Implementation of Queues

• Array implementation has issues:– Array size is fixed: only a finite number of queue elements

can be stored in it– Requires array to be treated in a special way, together with queueFront and queueRear

• Linked implementation of a queue simplifies many issues– Queue is never full because memory is allocated

dynamically


Linked Implementation of Queues (cont’d.)

• Elements are added at one end and removed from the other– Need only two pointers to maintain the queue: queueFront and queueRear


Empty and Full Queue

• Queue is empty if queueFront is NULL• Queue is never full

– Unless the system runs out of memory

• Note: must provide isFullQueue function definition because it is an abstract function in parent class queueADT


Initialize Queue

• Initializes queue to an empty state– Must remove all existing elements, if any– Deallocates memory occupied by elements


addQueue, front, back, and deleteQueue operations

• addQueue operation: adds new element to end of queue

• front operation: returns first element of queue• back operation: returns last element of queue• deleteQueue operation: removes first element of

queue



• Constructor– Accesses maxQueueSize, queueFront, and queueRear

• Destructor: destroys the queue– Deallocates memory occupied by elements

• Copy constructor and overloading assignment operator: – Similar to corresponding function for stack


Queue Derived from the class unorderedLinkedListType

• Linked implementation of queue: similar to implementation of a linked list created in a forward manner– addQueue similar to insertFirst– initializeQueue is like initializeList– isEmptyQueue similar to isEmptyList– deleteQueue can be implemented as before– queueFront is same as first– queueRear is same as last


Application of Queues: Simulation

• Simulation: a technique in which one system models the behavior of another system

• Computer models are used to study the behavior of real systems

• Queuing systems: computer simulations using queues as the data structure– Queues of objects are waiting to be served


Designing a Queuing System

• Server: object that provides the service• Customer: object receiving the service• Transaction time: service time, or the time it takes to

serve a customer• Model: system that consists of a list of servers and a

waiting queue holding the customers to be served– Customer at front of queue waits for the next available

server


Designing a Queuing System (cont’d.)

• Need to know:– Number of servers– Expected arrival time of a customer– Time between the arrivals of customers– Number of events affecting the system

• Performance of system depends on:– How many servers are available– How long it takes to serve a customer– How often a customer arrives


Designing a Queuing System (cont’d.)

• If it takes too long to serve a customer and customers arrive frequently, then more servers are needed – System can be modeled as a time-driven simulation

• Time-driven simulation: the clock is a counter– The passage of one unit of time can be implemented by

incrementing a counter by 1– Simulation is run for a fixed amount of time


Customer


Server


Server List

• Server list: a set of servers– At any given time, a server is either free or busy


Waiting Customers Queue

• When customer arrives, he/she goes to end of queue• When a server becomes available, customer at front

of queue leaves to conduct the transaction• After each time unit, the waiting time of each

customer in the queue is incremented by 1• Can use queueType but must add an operation to

increment waiting time


Main Program

• Algorithm for main loop:


Summary

• Stack: items are added/deleted from one end– Last In First Out (LIFO) data structure– Operations: push, pop, initialize, destroy, check for

empty/full stack– Can be implemented as array or linked list– Middle elements should not be accessed directly

• Postfix notation: operators are written after the operands (no parentheses needed)


Summary (cont’d.)

• Queue: items are added at one end and removed from the other end– First In First Out (FIFO) data structure– Operations: add, remove, initialize, destroy, check if queue

is empty/full– Can be implemented as array or linked list– Middle elements should not be accessed directly– Is a restricted version of array and linked list


chapter 17: stacks and queues

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